Related papers: Covering Distributions
Two-dimensional radiative transfer is employed to obtain the broad-band infrared spectrum of active galaxies. In the models we vary the geometry and size of the obscuring medium, the surface density, the opacity and the grain size…
One-point time-series measurements limit the observation of three-dimensional fully developed turbulence to one dimension. For one-dimensional models, like multiplicative branching processes, this implies that the energy flux from large to…
We study tori which are cyclic covers of the standard torus, that is, the deck transformation group of the covering map is cyclic. These covering tori can be parametrized in a natural way and we show that being cyclic is equivalent to…
We have found analytical expressions (polynomials) of the percolation probability for site percolation on a square lattice of size $L \times L$ sites when considering a plane (the crossing probability in a given direction), a cylinder…
Diffusion condensation is a dynamic process that yields a sequence of multiscale data representations that aim to encode meaningful abstractions. It has proven effective for manifold learning, denoising, clustering, and visualization of…
We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph G are either open or closed and refresh their status at rate \mu\ while at the same time a random walker moves on G at rate 1 but only along…
We discuss scaling limits of large bipartite quadrangulations of positive genus. For a given g, we consider, for every $n\ge1$, a random quadrangulation $\mathfrak{q}_n$ uniformly distributed over the set of all rooted bipartite…
We study the diffusion of a linear polymer in the presence of permeable membranes without excluded volume interactions, using scaling theory and Monte Carlo simulations. We find that the average time it takes for a chain with polymerization…
Coalescing-branching random walks, or {\em cobra walks} for short, are a natural variant of random walks on graphs that can model the spread of disease through contacts or the spread of information in networks. In a $k$-cobra walk, at each…
We study the phase transition of random radii Poisson Boolean percolation: Around each point of a planar Poisson point process, we draw a disc of random radius, independently for each point. The behavior of this process is well understood…
Consider two unit balls in a $d$-dimensional flat torus with edge length $r$, for $d\geq 2$. The balls do not move by themselves but they are pushed by a Brownian motion. The balls never intersect---they reflect if they touch. It is proved…
We consider a model system in which anomalous diffusion is generated by superposition of underlying linear modes with a broad range of relaxation times. In the language of Gaussian polymers, our model corresponds to Rouse (Fourier) modes…
The problem of drawing samples from a discrete distribution can be converted into a discrete optimization problem. In this work, we show how sampling from a continuous distribution can be converted into an optimization problem over…
By considering any one-dimensional time-homogeneous solvable diffusion process,this paper develops a complete analytical framework for computing the distribution of the last hitting time, to any level, and its joint distribution with the…
An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and…
Using a continuum bead-spring Monte Carlo model, we study the anomalous diffusion dynamics of a self-avoiding tethered membrane by means of extensive computer simulations. We focus on the subdiffusive stochastic motion of the membrane's…
Given a one-dimensional dynamical system we study its cover time, which quantifies the rate at which orbits become dense in the state space. Using transfer operator tools for dynamical systems with holes and inducing techniques, for a wide…
We use Langevin dynamics (LD) simulations to investigate single-file diffusion (SFD) in a dilute solution of flexible linear polymers inside a narrow tube with periodic boundary conditions (a torus). The transition from SFD, where the time…
The maximally compact representation of a regular orbit is in terms of its action-angle variables. Computing the map between a trajectory's Cartesian coordinates and its action-angle variables is called torus construction. This article…
Topology in quantum systems is typically considered in infinite crystals in one, two, or higher integer dimensions. Here, we show that one can continuously transform a system between a topological phase associated with one dimension and a…